Nah, don't. You know when people say, "don't change yourself for others"? Well, it's true. And this is the type of situation it points to. "Don't change yourself for others" doesn't work when it's used by people making excuses for things like being overweight. There's a difference between changing yourself and improving yourself.
Anyway, even if you do change yourself, I think you'll find that it's not worth it.
1. Forcibly altering your personality will get to you eventually. It will be an emotional burden just like when an introspective person forces himself to be extremely outgoing for long periods of time. It's exhausting.
2. If ever you alter it, and manage to attract someone, she won't be attracted to you, will she? Will you be able to keep up that facade forever?
3. Will you be attracted to her? You may like her on the outside, but if she meshes well with your "mature" persona, and not with your true, "goofy" persona, I don't really think it'll turn out well in the long term.
I'd say, stay true to yourself. Someone will come along who loves you and your personality. Just like there are different men, there are different women so it's not hard to imagine that you'll find someone young at heart like you. Lastly, mature isn't the right word, I think. For example, I like playing computer games and killing zombies (omgzombiesyay!) but that doesn't make me immature. I become immature when I prioritize killing zombies over more important responsibilities. No matter how much the zombies deserve to die (a lot). If it's truly maturity you think they're looking for, that will come with age and experience.
Good luck! :D